{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import factorial\n",
    "from math import log\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "comb = lambda a, b: factorial(a)/factorial(b)/factorial(a-b)\n",
    "def fn(d):\n",
    "    r = comb(1000, d)\n",
    "    for _ in xrange(1000):\n",
    "        r /= 2.0\n",
    "    return r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = range(1001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = [fn(x) for x in d]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "intp = [0]\n",
    "for idx, x in enumerate(p):\n",
    "    intp.append(intp[idx] + x)\n",
    "intp = intp[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
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       " (914, -0.0),\n",
       " (915, -0.0),\n",
       " (916, -0.0),\n",
       " (917, -0.0),\n",
       " (918, -0.0),\n",
       " (919, -0.0),\n",
       " (920, -0.0),\n",
       " (921, -0.0),\n",
       " (922, -0.0),\n",
       " (923, -0.0),\n",
       " (924, -0.0),\n",
       " (925, -0.0),\n",
       " (926, -0.0),\n",
       " (927, -0.0),\n",
       " (928, -0.0),\n",
       " (929, -0.0),\n",
       " (930, -0.0),\n",
       " (931, -0.0),\n",
       " (932, -0.0),\n",
       " (933, -0.0),\n",
       " (934, -0.0),\n",
       " (935, -0.0),\n",
       " (936, -0.0),\n",
       " (937, -0.0),\n",
       " (938, -0.0),\n",
       " (939, -0.0),\n",
       " (940, -0.0),\n",
       " (941, -0.0),\n",
       " (942, -0.0),\n",
       " (943, -0.0),\n",
       " (944, -0.0),\n",
       " (945, -0.0),\n",
       " (946, -0.0),\n",
       " (947, -0.0),\n",
       " (948, -0.0),\n",
       " (949, -0.0),\n",
       " (950, -0.0),\n",
       " (951, -0.0),\n",
       " (952, -0.0),\n",
       " (953, -0.0),\n",
       " (954, -0.0),\n",
       " (955, -0.0),\n",
       " (956, -0.0),\n",
       " (957, -0.0),\n",
       " (958, -0.0),\n",
       " (959, -0.0),\n",
       " (960, -0.0),\n",
       " (961, -0.0),\n",
       " (962, -0.0),\n",
       " (963, -0.0),\n",
       " (964, -0.0),\n",
       " (965, -0.0),\n",
       " (966, -0.0),\n",
       " (967, -0.0),\n",
       " (968, -0.0),\n",
       " (969, -0.0),\n",
       " (970, -0.0),\n",
       " (971, -0.0),\n",
       " (972, -0.0),\n",
       " (973, -0.0),\n",
       " (974, -0.0),\n",
       " (975, -0.0),\n",
       " (976, -0.0),\n",
       " (977, -0.0),\n",
       " (978, -0.0),\n",
       " (979, -0.0),\n",
       " (980, -0.0),\n",
       " (981, -0.0),\n",
       " (982, -0.0),\n",
       " (983, -0.0),\n",
       " (984, -0.0),\n",
       " (985, -0.0),\n",
       " (986, -0.0),\n",
       " (987, -0.0),\n",
       " (988, -0.0),\n",
       " (989, -0.0),\n",
       " (990, -0.0),\n",
       " (991, -0.0),\n",
       " (992, -0.0),\n",
       " (993, -0.0),\n",
       " (994, -0.0),\n",
       " (995, -0.0),\n",
       " (996, -0.0),\n",
       " (997, -0.0),\n",
       " (998, -0.0),\n",
       " (999, -0.0),\n",
       " ...]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(enumerate(intI))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "I = [-log(x)/log(2) for x in p]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "intI = [-log(x)/log(2) for x in intp]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(21.58433363061018, 12.240997780509938)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "I[425], I[451]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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56aSTsi5JkiSpJFlfkVUG8sML2traMq5EkiSpdAbZOuQNX5IkqRYYZOtQ/orsqlWr2L59e8bVSJIklcYgW4cmTJjAm970Jvbu3cvDDz+cdTmSJEklMcjWKYcXSJKkameQrVM+4UuSJFU7g2ydyl+RbWtrI6WUcTWSJEm9Z5CtU2eeeSZNTU1s3ryZZ599NutyJEmSes0gW6cGDx5Mc3Mz4PACSZJUnQyydaxweIEkSVK1McjWMW/4kiRJ1cwgW8fyV2RXrFjBzp07M65GkiSpdwyydWzSpEmMGTOGXC7HI488knU5kiRJvWKQrWMR4fACSZJUtQyydc4bviRJUrUyyNY5r8hKkqRqZZCtc7NmzWLAgAFs2LCBDRs2ZF2OJElSjxlk69zQoUOZPn06ANOnT2fs2LHMmjWLF198MePKJEmSDs4gKy688EIAXn75ZTZv3szy5cu58847M65KkiTp4Ayy4uqrr+aJJ55g5cqVfOITnwAcMytJkiqfQVZEBKeccgrTp0/nggsuAAyykiSp8hlktZ85c+YAsHr1arZt25ZxNZIkScUZZLWfcePGMWnSJPbt28eyZcuyLkeSJKkog6wOkH9IgsMLJElSJTPI6gD5hyT4tC9JklTJDLI6QOHTvlJKGVcjSZLUPYOsDnDmmWcyaNAgtm7dyrp167IuR5IkqVsGWR1g4MCBzJgxA3B4gSRJqlwGWXWrcHiBJElSJTLIqlv5mQseeughXn/99f1eO3fuzLg6SZIkg6yKyF+RXbFiBUOGDNnvNXjwYK666qqMK5QkSfXOIKtuTZw4kXPPPbfo+ptvvtkZDSRJUqYasy5AlWvRokVs3759v2W7du1i3LhxbN68mWeeeYbJkydnVJ0kSap3XpFVURHBkUceud/rmGOOobm5GfBGMEmSlC2DrHrNR9hKkqRKYJBVr/kIW0mSVAkMsuq1whkNXn/99YyrkSRJ9cogq147/vjjGTNmDHv27GHFihVZlyNJkuqUQVa9FhEOL5AkSZkzyKokPsJWkiRlzSCrkjhzgSRJyppBViWZNWsWDQ0NbNiwgQ0bNmRdjiRJqkMGWZVk6NChTJ8+HYAf/ehHrFmzxkArSZLKyiCrkuWHF3zmM59h2rRpTJw4kZ/+9KcZVyVJkuqFQVYlu+SSS5gyZQqjRo1iyJAhAPzkJz/JuCpJklQvDLIq2ezZs1m7di1btmzh+9//PuB0XJIkqXwMsuoT+em4Vq9ezbZt2zKuRpIk1QODrPrEuHHjmDRpEiklli1blnU5kiSpDhhk1Wd82pckSSong6z6jA9JkCRJ5WSQVZ8pfGxtSinjaiRJUq0zyKrPNDc3M3DgQLZu3cratWuzLkeSJNU4g6z6zKBBg5g5cybg8AJJktT/Mg2yEXFVRCyLiG0R8UJE3B4Rp3TZ5oiIuCEiXoyI1yLitogYk1XNOjhv+JIkSeWS9RXZc4AbgLnAPKAJuDsihhZscy3wXuCPOrcfD/yozHWqhwrHyUqSJPWnxiwPnlJ6d+H7iPgY8AIwE/hVRIwALgXmp5Tu7dzmEuDxiJibUjItVZj8zAUrV67kjjvuYMCAAUydOpUTTzwx48okSVKtyTTIdmNE58+XOn/OpOMq7T35DVJKT0TEc0ArcECQjYhBwKCCRcMAcrkcuVyuP2reT/4Y5ThWJRozZgzjx49n48aNvP/97wdg6NChrF27lmHDhgH125uDqffz5mDsTffsS3H2pjh7U5y9Ka4cvSl131Ep0yRFRANwJzAypXRW57L5wM0ppUFdtl0K3JdS+vNu9vMl4OquyxcsWMCQIUP6o3R1cd9997Fw4UL27dvH+vXr2blzJ1/4wheYNWtW1qVJkqQKtGPHDubPnw8wIqXU3tPPVdIV2RuAacBZh7mfvwG+UfB+GLDhXe96F8OHDz/MXR9aLpdj0aJFzJs3j6ampn4/XiW64IIL+Lu/+zsA/uRP/oTvfe977N27l3nz5tV9b4rxvCnO3nTPvhRnb4qzN8XZm+LK0Zv29h5n1/1URJCNiOuB/wS8LaW0oWDVJmBgRIxMKb1SsHxM57oDpJR2AbsK9g1AU1NTWU/Mch+vUr3lLW/he9/7HkuXLn2jH/amOHtTnL3pnn0pzt4UZ2+KszfF9WdvSt1v1tNvRWeI/QDwzpTS0102WQ7kgHMLPnMKcBzg/E5VID+LwdKlS9m7d2/G1UiSpFqS9RXZG4D5wPuAbRExtnP5qyml11NKr0bEd4FvRMRLQDvwbaDNGQuqw7Rp0xg6dCjbtm3j8ccfz7ocSZJUQ7KeR/ZTdMxUcD/wfMHr4oJtrgR+CtwG/IqOIQV/WNYqVbIBAwbQ0tICwJIlSzKuRpIk1ZJMg2xKKYq8/rlgm50ppctTSkenlIamlP4wpdTt+FhVpvzwAoOsJEnqS1lfkVUdyD8kwSArSZL6kkFW/W7OnDkAPP7447z22msZVyNJkmqFQVb9bvTo0UyZMgWA3/72txlXI0mSaoVBVmWRH17w1FNPZVyJJEmqFQZZlUX+hq/Fixdzww03cOONN7J+/fqMq5IkSdUs63lkVSfyV2SffvpprrzySgBuu+02fvGLX2RZliRJqmJekVVZzJgxg2uuuYazzjqLCy+8EICHHnqI3bt3Z1yZJEmqVl6RVVlEBFdddRVnnHEG559/PmPHjuXll19m5cqVzJ49O+vyJElSFSo5yEbEucC5wGi6XNlNKX38MOtSDYsI5s6dy89//nMWL15skJUkSSUpaWhBRFwN3E1HkB0FHNXlJR1Ufszs4sWLM65EkiRVq1KvyH4S+FhK6V/6shjVj/wsBm1tbRlXIkmSqlWpN3sNBB7qy0JUX1paWogInn76aTZv3px1OZIkqQqVGmS/A8zvy0JUX0aMGMFpp50GwJIlSzKuRpIkVaNShxYcAVwWEecBq4Bc4cqU0mcPtzDVvrlz57JmzRra2tremJJLkiSpp0q9Ijsd+A2wD5gGnFnwau6b0lTrCp/2JUmS1FslXZFNKb2jrwtR/cnPXLBs2TL27NlDY6PTGkuSpJ477Cd7RcSEiJjQF8Wovpx66qkMHz6c7du3s3r16qzLkSRJVabUeWQbIuKLEfEq8CzwbES8EhF/FRE+9lY90tDQQEtLCwBXXXUVV155Jddccw3btm3LuDJJklQNSv1d7l8DlwJ/ATzYuews4Et03Aj2l4ddmerC2WefzT333MPChQtZuHAhAMOGDeOzn/V+QUmSdHClBtn/AvxJSunOgmWrIuJ3wI0YZNVDn/nMZ2hqamLbtm2sWLGChQsX8sADDxhkJUnSIZUaZI8Gnuhm+ROd66QeGTFiBFdddRUADzzwAAsXLqStrY2UEhGRcXWSJKmSlTqedSVwRTfLr+hcJ/XazJkzaWxsZNOmTaxfvz7rciRJUoUrNch+Hvh4RDwWEd/tfD0GfAz4H31WnerK4MGDaW7umIa4ra0t42okSVKlKynIppR+CZwM/BgY2fn6EXBKSunXfVee6o0PSZAkST1V8gz0KaWNeFOX+lhrayvXX3+9QVaSJB1Sj4NsREwHVqeU9nX+uaiU0qrDrkx1KX9F9pFHHmHXrl0MGjQo44okSVKl6s0V2d8AY4EXOv+cgO5uK0/AgMMvTfVo8uTJHHvssWzZsoUVK1a8EWwlSZK66s0Y2cnAloI/T+n82fU1pS8LVH2JCFpbWwHHyUqSpIPrcZBNKT2bUkqdbycBv+tc9sYL+F3nOqlk+auwzlwgSZIOptTpt+6j+wcfjOhcJ5XMmQskSVJPlDprQdAxFrarY4DtpZcjwezZs2loaOC5557jwgsvpKFh///e+uAHP8hHP/rRjKqTJEmVoldBNiJ+1PnHBPxzROwqWD0AmA481Ee1qU4deeSRtLS0sHjxYn7yk58csP6uu+7i4osvZuDAgRlUJ0mSKkVvr8i+2vkzgG3A6wXrdgOLgX/qg7pU5/7t3/6Nu+++m3379u23/M///M95+eWXWblyJbNnz86oOkmSVAl6FWRTSpcARMQzwNdTSg4jUL+YOHEil1566QHLb7/9dn72s5+xePFig6wkSXWu1EfUXmOIVRac0UCSJOWV/IjaiLgI+BBwHLDfYMWU0ozDrEvqljMaSJKkvJKuyEbEp4Gbgc3AmcBS4EU6Hobw8z6rTuqipaWFiODpp59m8+bNWZcjSZIyVOo8sn8GXJZS+q903OT1tZTSPOA6OuaSlfrFiBEjOO200wCvykqSVO9KDbLH8ftptl4HhnX++V+AjxxuUdLBOLxAkiRB6UF2E79/stdzwNzOP0+mY2ouqd+0trYCBllJkupdqUH2XuDCzj/fDFwbEYuAHwI/7ovCpGLyV2SXLl3Knj17Mq5GkiRlpdRZCy6jMwSnlG6IiBeBtwB3Av/QR7VJ3Tr11FMZPnw47e3trF69mubm5qxLkiRJGSh1Htl9KaU9Be9vTSl9OqX07ZTS7r4rTzpQQ0MDc+bMARxeIElSPSt1aAERcUREtETEf4qICwtffVmg1J388IK/+qu/Yvr06bS0tPDrX/8646okSVI5lTS0ICLeDXwPGNXN6gQMOJyipEP5gz/4A77yla+wdetWtm7dCsC1117L2WefnXFlkiSpXEq9Ivtt4P8A41JKDV1ehlj1u7e+9a2sWrWKRYsWcf311wMdj61NKWVcmSRJKpdSg+wY4BspJR+tpMy8+c1v5rzzzuOSSy6hsbGRTZs28dxzz2VdliRJKpNSg+z/D7y9D+uQSjZkyBDOOOMMwJu/JEmqJ6VOv3UF8H8i4mzgUSBXuDKldN3hFib1RmtrK8uXL2fx4sVcfPHFWZcjSZLKoNQg+xHgXcBOOq7MFg5MTIBBVmU1d+5crr/+etra2rIuRZIklUmpQfavgauBv00p7evDeqSS5KfjWrFiBbt27WLQoEEZVyRJkvpbqWNkBwI/NMSqUkyZMoVjjz2W3bt3s2LFiqzLkSRJZVBqkL0FcCCiKkZEvHFV1uEFkiTVh1KD7ADg8xHxy4j4dkR8o/DV051ExNsi4icRsTEiUkS8v8v6f+5cXvhaWGLNqnH5IOvMBZIk1YdSx8i+Gcj//nZal3W9mZF+KLASuAn4UZFtFgKXFLzf1Yv9q460trYCBllJkupFSUE2pfSOvjh4SunnwM+h41fDRexKKW3qi+Opts2aNYuGhgaee+45Nm7cyPjx47MuSZIk9aNeB9mIaAJeB5pTSqv7vqQDvD0iXgBeBu4FvpBSevEg9Q0CCm9ZHwaQy+XI5XLdf6gP5Y9RjmNVm/7uzRFHHMHpp5/Oo48+yoknnsiAAfs/LXn27Nn8+7//O42Npf4iov943hRnb7pnX4qzN8XZm+LsTXHl6E2p+45Snk0fEeuAD6SUVpZ01O73mTr3eXvBsg8DO4CngROA/wm8BrSmlPYW2c+X6JgabD8LFixgyJAhfVWuKtQPf/hD/vVf/7Xo+q9//euceOKJZaxIkiQdyo4dO5g/fz7AiJRSe08/V2qQvRT4Q+CjKaWXer2D7vd5QJDtZpspwFrgvJTSL4ps090V2Q1bt25l+PDhfVHqQeVyORYtWsS8efNoamrq9+NVk3L1ZsOGDezevXu/ZZ/61Ke47777uPbaa7n88sv77dil8rwpzt50z74UZ2+KszfF2ZviytGb9vZ2Ro0aBb0MsofziNoTgY0R8SywvXBlSmlGifs9qJTSuojY2nnsboNsSmkXBTeE5cfeNjU1lfXELPfxqkl/92by5MkHLHv729/Offfdx7Jlyyr638Xzpjh70z37Upy9Kc7eFGdviuvP3pS631KDbNGrpv0pIiYAxwDPZ3F8VS9nNJAkqfaUOmvBNX1x8Ig4ko6rq3mTI6IZeKnzdTVwG7CJjjGyXwP+A7irL46v+tHS0kJEsG7dOl544QVGjx6ddUmSJOkwlfpABAAiYmZE/OfO15kl7GIWHfPR5uek/Ubnn78M7AWmA3cCTwHfBZYDZ3cOH5B6bMSIEZx66qmAV2UlSaoVJV2RjYjRwK3A24FXOhePjIj7gA+nlLb0ZD8ppfuBohPIAn9QSn1Sd1pbW3nsscdYvHgxF154YdblSJKkw1TqFdlv0zEbwOkppaNTSkfT8YSv4cAAqn7UAAAgAElEQVR1fVWc1Jfyj7Bta2vLuBJJktQXSr3Z6910TIH1eH5BSumxiLgcuLtPKpP6WD7ILlu2jD179lTkgxEkSVLPlXpFtgHo7hEMucPYp9SvTjvtNIYPH8727dtZs2ZN1uVIkqTDVGrovBf4VkS88TD7iHgTcC1F5neVstbQ0EBLSwvg8AJJkmpBqUH2CjrGwz4TEWsjYi0dj5EdDvzXvipO6mv54QW//OUv2bJlCy+91CcPppMkSRkoKcimlNYDM4D3AN/sfF2QUpqRUtrQh/VJfSr/YIRbb72V0aNHc8wxx/C5z30u46okSVIpehxkI+KliBjV+eebgCNTSotSSt/ufN3Tb1VKfeRtb3vbG/PJ5i1YsICUUkYVSZKkUvXmiuxAOoYOAPwX4Ii+L0fqX0ceeSRr1qxh3759vPbaazQ2NvL888+zfv36rEuTJEm91Jv5h9qA2yNiOR0PMbguIl7vbsOU0sf7ojipP0R0PINj6NChnHHGGSxfvpzFixdz3HHHZVyZJEnqjd5ckf3PwM+AI4EEjACOKvKSqoIPSZAkqXr1+IpsSmkz8BcAEfE08NGU0ov9VZhUDnPnzuWGG25g8eLFWZciSZJ6qaRHG6WUJvd1IVIW8rMYPPLII+zatYtBgwZlXJEkSeqpkp/RGRHnAucCo+kyRMExsqoWU6ZMYdSoUWzdupUVK1a8MdRAkiRVvpLmkY2Iq4G76Qiyo3CMrKpURLwRXh1eIElSdSn1iuwngY+llP6lL4uRstDa2spPf/pTg6wkSVWm1EfUDgQe6stCpKw4c4EkSdWp1CD7HWB+XxYiZWX27Nk0NDTw3HPPsXHjxqzLkSRJPVTq0IIjgMsi4jxgFZArXJlS+uzhFiaVy7Bhw5g2bRqrVq3i1ltv5ayzztpv/fjx45kwYUJG1UmSpGJKDbLTgd90/nlaH9UiZWbu3LmsWrWK//7f//sB6wYMGMBjjz3GySefnEFlkiSpmFLnkX1HXxciZemyyy6jra2Nbdu27bd8y5YtbN++nbvvvtsgK0lShelVkI2IH/Vgs5RS+mCJ9UiZmDlzJqtWrTpg+Ve+8hW++MUvsnjxYq644ooMKpMkScX09orsq/1ShVShnNFAkqTK1asgm1K6pL8KkSpRS0sLEcG6det44YUXGD16dNYlSZKkTqVOvyXVhREjRnDaaacBsGTJkoyrkSRJhQyy0iE4vECSpMpkkJUOIR9kfYStJEmVxSArHUJraysAS5cuZe/evRlXI0mS8gyy0iGceuqpDB8+nO3bt7N69eqsy5EkSZ0MstIhNDQ0MGfOHMDhBZIkVRKDrNQD3vAlSVLlKekRtVK9yQfZ+++/n1tvvXW/dQMGDODcc8/l6KOPzqI0SZLqlkFW6oF8kH322Wf5yEc+csD6973vfdx+++3lLkuSpLpmkJV64Oijj+arX/0qCxcu3G/5rl27eOihh7j33nvZu3cvAwYMyKhCSZLqj0FW6qHPf/7zfP7zn99v2Z49exg5ciTbtm3j8ccfZ9q0aRlVJ0lS/fFmL+kwNDY2Mnv2bMAZDSRJKjeDrHSY8g9MMMhKklReBlnpMDk1lyRJ2TDISocpH2Qfe+wxXnnllYyrkSSpfhhkpcM0evRopkyZAsCyZcsyrkaSpPphkJX6gMMLJEkqP4Os1AfyQdYbviRJKh+DrNQHCmcuSCllXI0kSfXBICv1genTp3PEEUfw8ssv89RTT2VdjiRJdcEne0l9YODAgcycOZMHH3yQL3/5ywc84ev444/nwx/+MBGRUYWSJNUeg6zUR9761rfy4IMPsmDBgm7XT5w4kbPOOqvMVUmSVLsMslIfufLKK9m9ezfbtm3bb/mDDz7IE088wa9+9SuDrCRJfcggK/WRsWPHcu211x6w/Jvf/CZXXnmlMxpIktTHvNlL6meFc8w6o4EkSX3HICv1szPPPJOBAweydetW1q1bl3U5kiTVDIOs1M8GDRrEjBkzAB+YIElSXzLISmXgI2wlSep7BlmpDHyErSRJfc8gK5VB/hG2K1euZMeOHRlXI0lSbTDISmUwceJExo0bx549e1i+fHnW5UiSVBMyDbIR8baI+ElEbIyIFBHv77I+IuLLEfF8RLweEfdExElZ1SuVKiIcXiBJUh/L+orsUGAlcHmR9Z8HPg18EpgDbAfuiogjylOe1HfywwsMspIk9Y1Mn+yVUvo58HPouGJVKDoW/Dfg/0sp3dG57P8BNgPvB27tbp8RMQgYVLBoGEAulyOXy/Xx3+BA+WOU41jVpt57M2vWLADuvfdeLr300v3WRQSnnnpq3fbmYOr9vCnGvhRnb4qzN8XZm+LK0ZtS9x2V8qShiEjAB1JKt3e+nwKsBc5MKf2mYLtfAr9JKX2myH6+BFzddfmCBQsYMmRIf5Qu9ciuXbv46Ec/yu7du7tdf8opp/DVr361zFVJkpS9HTt2MH/+fIARKaX2nn6ukoPsW4AHgfEppecLtvs3IKWULi6yn+6uyG7YunUrw4cP77f683K5HIsWLWLevHk0NTX1+/Gqib2BX//61zzwwAP7Ldu+fTtf+9rXaGxs5IUXXuDII4/MqLrK5HnTPftSnL0pzt4UZ2+KK0dv2tvbGTVqFPQyyGY6tKA/pJR2Abvy7/NDFpqamsp6Ypb7eNWknnvzzne+k3e+8537LUspcfPNN7NlyxbWrFnDWWedlVF1la2ez5uDsS/F2Zvi7E1x9qa4/uxNqfvN+mavg9nU+XNMl+VjCtZJVS8iaGlpAbwRTJKk3qjkIPs0HYH13PyCiBhOx+wFPudTNWXOnDkALFmyJONKJEmqHpkOLYiII4ETCxZNjohm4KWU0nMR8U3gCxHxWzqC7VeAjcDt5a9W6j/5OWaXLl2acSWSJFWPrMfIzgLuK3j/jc6ftwAfA75Gx1yz/wiMBB4A3p1S2lnGGqV+N3PmTBoaGnjuuefYuHEj48ePz7okSZIqXqZDC1JK96eUopvXxzrXp5TSF1NKY1NKR6SUzkspPZVlzVJ/GDZsGMcddxzgOFlJknqqksfISnXllFNOAQyykiT1lEFWqhAnn3wyAG1t3ssoSVJPGGSlCjF16lQAHn74YR+RKElSDxhkpQoxbtw4jjrqKHbu3MnKlSuzLkeSpIqX9awFkjo1NDTQ0tLCXXfdxcc+9jHGjh273/rjjz+eG2+8kYEDB2ZUoSRJlcUgK1WQd77zndx1112sWbOGNWvWHLD+wgsv5MILL8ygMkmSKo9BVqogl19+OaeeeiqvvfbafstvueUW7rrrLtra2gyykiR1MshKFWTgwIG8973vPWD5jh07uOuuu5yaS5KkAt7sJVWB1tZWAJYtW8aePXsyrkaSpMpgkJWqwNSpUxk+fDjbt29n9erVWZcjSVJFMMhKVaChoYE5c+YAPvlLkqQ8g6xUJfLDCwyykiR1MMhKVWLu3LmAQVaSpDyDrFQl8kMLnnzySV566aWMq5EkKXsGWalKHH300ZxyyikALFmyJONqJEnKnkFWqiIOL5Ak6fcMslIVyQfZtra2jCuRJCl7PtlLqiL5mQvuu+8+TjjhhKLbDR48mBtuuIFzzjmnXKVJklR2Blmpipx++ulMnDiR9evXs27duoNua5CVJNU6g6xURRobG1m1ahVPPPFE0W0effRRLrvsMocfSJJqnkFWqjIjR458Y6xsd9785jfzyU9+kg0bNrBhwwYmTJhQxuokSSofb/aSaszQoUOZPn064OwGkqTaZpCVapDTdEmS6oFBVqpB+dkNDLKSpFpmkJVqUP6K7MMPP8zu3bszrkaSpP5hkJVq0EknncTRRx/Nrl27WLlyZdblSJLULwyyUg2KCMfJSpJqnkFWqlE+zlaSVOsMslKN8oqsJKnWGWSlGtXS0kJE8PTTT7N58+asy5Ekqc8ZZKUaNWLECE477TQAxo4dS0QUfX384x/PuFpJknrPICvVsI985CM92u573/se27dv7+dqJEnqWwZZqYb95V/+JS+99BKbN28u+ho/fjx79+5l+fLlWZcrSVKvNGZdgKT+ddRRRx10fWtrK7fddhttbW287W1vK1NVkiQdPq/ISnXO2Q0kSdXKICvVudbWVqAjyKaUMq5GkqSeM8hKdW7GjBk0NjayadMmnn322azLkSSpxwyyUp0bPHgwzc3NgMMLJEnVxSArab/hBZIkVQuDrKQ3bvhqa2vLuBJJknrOICvpjSC7YsUKdu7cmXE1kiT1jEFWEpMnT2b06NHkcjlWrFiRdTmSJPWID0SQREQwd+5c7rzzThYuXMi4ceOKbjtq1CiOPPLIMlYnSVL3vCIrCfj98IIvf/nLTJ48uehr3LhxbNiwIeNqJUkyyErq9KEPfYhJkyYxZMiQoq+GhgZee+01Fi1alHW5kiQZZCV1OOGEE3jmmWfYvn170dfnPvc5wNkNJEmVwSArqcfyww+cb1aSVAkMspJ6LB9kV69ezbZt2zKuRpJU7wyyknps3LhxTJo0iZQSS5cuzbocSVKdM8hK6hWHF0iSKoVBVlKvtLa2AgZZSVL2DLKSeqXwimxKKeNqJEn1zCArqVeam5sZOHAgW7duZe3atVmXI0mqYxUdZCPiSxGRuryeyLouqZ4NGjSImTNnAg4vkCRlq6KDbKc1wLiC11nZliMpP7zAByNIkrLUmHUBPbAnpbQp6yIk/V4+yN5///3ce++9PfrMMcccw/Tp04mI/ixNklRHqiHInhQRG4GdQBtwVUrpuWIbR8QgYFDBomEAuVyOXC7Xr4Xmj1P4U79nb4qrtt7MmjULgMcee4xzzz23x5+74447OP/883t1rGrrTbnYl+LsTXH2pjh7U1w5elPqvqOS7zqOiPOBI4En6RhWcDXwJmBaSqnbxwpFxJc6t9vPggULGDJkSP8VK9WRlBLf/e53WbVqVY+2f/XVV3n11Vd5z3vewyc+8Yl+rk6SVG127NjB/PnzAUaklNp7+rmKDrJdRcRI4Fngsyml7xbZprsrshu2bt3K8OHD+73GXC7HokWLmDdvHk1NTf1+vGpib4qr9d788Ic/5KMf/SgzZ87s9bjaWu9NqexLcfamOHtTnL0prhy9aW9vZ9SoUdDLIFsNQwvekFJ6JSKeAk48yDa7gF359/nxeE1NTWU9Mct9vGpib4qr1d6cffbZAKxcuZI9e/YwePDgXu+jVntzuOxLcfamOHtTnL0prj97U+p+q2HWgjdExJHACcDzWdciqeeOO+44xo4dy549e1i+fHnW5UiSakRFB9mI+HpEnBMRx0fEW4AfA3uBf824NEm9EBH7PRFMkqS+UNFBFphAR2h9Evg34EVgbkppS6ZVSeq11tZWwCArSeo7FT1GNqX04axrkNQ3Ch+ikFJyPllJ0mGr9CuykmrEzJkzGTBgABs3bmTDhg1ZlyNJqgEGWUllMXToUM444wzA4QWSpL5hkJVUNoXDCyRJOlwGWUll48wFkqS+VNE3e0mqLfmZC5YvX853vvOdHt3wNXDgQAYNGnTI7SRJ9ccgK6lsTjjhBEaNGsXWrVv5xCc+0ePPfehDH+IDH/hAP1YmSapGBllJZRMR/K//9b/4l3/5F1JKh9x+06ZNLFu2jEcffbQM1UmSqo1BVlJZXXTRRVx00UU92vbJJ59k6tSprF27llwu5/PPJUn78WYvSRXrpJNO4qijjmL37t2sWrUq63IkSRXGICupYjU0NNDS0gLAkiVLMq5GklRpDLKSKtqcOXMAg6wk6UAGWUkVzSArSSrGICupos2ePRuAdevW8cILL2RcjSSpkhhkJVW0kSNHMnHiRMCrspKk/RlkJVW8k08+GYC2traMK5EkVRKDrKSKd8oppwCwePHijCuRJFUSg6ykipcPskuXLmXv3r0ZVyNJqhQ+2UtSxZswYQLDhg1j27ZtfPrTn2bkyJG9+vyQIUP40z/9U0aNGtVPFUqSsmCQlVTxBgwYQGtrK3fffTc33nhjSft46aWX+Pu///s+rkySlCWDrKSq8PWvf51bbrmFXC7Xq88988wz3HnnnTzwwAP9VJkkKSsGWUlVYerUqXz961/v9eeefvpp7rzzTlasWMHOnTs54ogj+qE6SVIWvNlLUk07/vjjGT16NLlcjkceeSTrciRJfcggK6mmRQStra2A03dJUq0xyEqqeXPnzgV8oIIk1RqDrKSalw+yXpGVpNpikJVU82bPnk1DQwMbNmxgw4YNWZcjSeojBllJNW/o0KFMnz4d8KqsJNUSg6ykuuDwAkmqPQZZSXXBmQskqfYYZCXVhfwV2Ycffpjdu3dnXI0kqS/4ZC9JdeGkk07i6KOP5qWXXuKDH/wgw4YNK3lfo0aN4q//+q8Pax+SpMNnkJVUFyKCc845hx//+Mf89Kc/Pez9TZ06lT/7sz/rg8okSaUyyEqqGzfccAPnnXceuVyu5H3cd9993HHHHTz00EMGWUnKmEFWUt0YN27cYYfPqVOncscdd3jTmCRVAG/2kqRemDNnDgBr165ly5YtGVcjSfXNICtJvTBy5EhOPfVUwKm8JClrBllJ6iUfriBJlcEgK0m95MMVJKkyGGQlqZfyV2SXLl3K3r17M65GkuqXQVaSeum0005j2LBhvPbaa6xZsybrciSpbhlkJamXBgwYQEtLC+DwAknKkkFWkkqQH17Q1taWcSWSVL8MspJUAm/4kqTs+WQvSSpB/sEITzzxxBtXZ8th6NChfPOb32Tq1KllO6YkVSqDrCSVYNSoUcyYMYNHHnmEJUuWlPXY1113HTfeeGNZjylJlcggK0klWrhwIYsXLyalVJbjPfLII1xzzTUOZ5CkTgZZSSrRsccey3vf+96yHa+lpYVrrrmGNWvW0N7eXrbjSlKl8mYvSaoSY8eO5fjjjyelxLJly7IuR5IyZ5CVpCqSv7Gs3ONyJakSGWQlqYrkp/1aunRpxpVIUvYMspJURQqvyJbrJjNJqlQGWUmqIs3NzQwaNIgXX3yR559/PutyJClTBllJqiIDBw5k5syZADz55JMZVyNJ2aqKIBsRl0fEMxGxMyKWRERL1jVJUlbywwsMspLqXcUH2Yi4GPgGcA0wA1gJ3BURozMtTJIykg+yTz31VMaVSFK2Kj7IAp8F/imldHNK6THgk8AO4OPZliVJ2cjPXPDMM8+wffv2jKuRpOxU9JO9ImIgMBP4m/yylNK+iLgHaC3ymUHAoIJFwwByuRy5XK4fq+2QP0Y5jlVt7E1x9qY4e3OgMWPGMH78eDZu3MgJJ5xAY2NFf5WXXUqJ3bt3M3DgQCIi63Iqir0pzt4caPbs2fz4xz8uy/dwqfuu9G+/UcAAYHOX5ZuBqUU+cxVwddeFd999N0OGDOnb6g5i0aJFZTtWtbE3xdmb4uzN/s444ww2btzISy+9lHUpkmrUunXr+NnPfvbG+/78Ht6xY0dJn4tKnocwIsYDvwPeklJqK1j+NeCclNKcbj7T3RXZDVu3bmX48OH9XTK5XI5FixYxb948mpqa+v141cTeFGdvirM33du1axe33HILLS0tXpHtYs+ePbS1tdHa2mpvurA3xdmbAw0ZMoQpU6aU5Xu4vb2dUaNGAYxIKbX39HOV/i+1FdgLjOmyfAywqbsPpJR2Abvy7/O/Hmhqairr/wmW+3jVxN4UZ2+KszcHmjBhAs3Nzfali1wux8aNG+1NN+xNcfbm0Prze7jU/Vb0zV4ppd3AcuDc/LKIaOh831bsc5IkSap9lX5FFjqm3rolIh4GlgL/DRgK3JxpVZIkScpUxQfZlNIPI+JY4MvAWOA3wLtTSl1vAJMkSVIdqfggC5BSuh64Pus6JEmSVDkqeoysJEmSVIxBVpIkSVXJICtJkqSqZJCVJElSVTLISpIkqSoZZCVJklSVDLKSJEmqSgZZSZIkVSWDrCRJkqqSQVaSJElVySArSZKkqmSQlSRJUlUyyEqSJKkqNWZdQLm0t7eX5Ti5XI4dO3bQ3t5OU1NTWY5ZLexNcfamOHvTPftSnL0pzt4UZ2+KK0dvSs1pkVLq41IqS0S8CdiQdR2SJEk6pAkppd/1dON6CLIBjAe2lemQw+gIzhPKeMxqYW+KszfF2Zvu2Zfi7E1x9qY4e1NcuXozDNiYehFOa35oQWczepzsD1dHbgZgW0qpPOMZqoS9Kc7eFGdvumdfirM3xdmb4uxNcWXsTa/37c1ekiRJqkoGWUmSJFUlg2zf2wVc0/lT+7M3xdmb4uxN9+xLcfamOHtTnL0prmJ7U/M3e0mSJKk2eUVWkiRJVckgK0mSpKpkkJUkSVJVMshKkiSpKhlkSxARfxERKSK+WbDsiIi4ISJejIjXIuK2iBjT5XPHRcS/R8SOiHghIv4uImrmoRRd+xIRR0fEtyPiyYh4PSKei4jrImJEl8+lbl4fzuZv0T+KnDP3d/P3/t9dPlfT5wx0e94cX+ScSBHxRwWfq7nzJiK+1M3f6YmC9XX7PXOw3tT7d00Pzpu6/a45xHlTt981ABHxpoj4fuf3yesR8WhEzCpYHxHx5Yh4vnP9PRFxUpd9HB0RP4iI9oh4JSK+GxFHlvPvUfUnablFxGzgT4FVXVZdC7wH+CPgVeB64EfAWzs/NwD4d2AT8BZgHPA9IAf8v+WovT8V6cv4ztfngMeAScD/7lx2UZddXAIsLHj/Sr8VW2YHOWcA/gn4YsH7HQWfq+lzBor2Zj0df9dClwH/A/h5l+W1eN6sAc4reL+n4M91/T1D8d74XXPw8wbq+7umWG/q9rsmIo4CHgTuA84HtgAnAS8XbPZ54NPAfwGeBr4C3BURp6WUdnZu8wM6ejgPaAJuBv4RmF+Gv0aHlJKvHr6AI4Gn6PgfxP3ANzuXjwB2AxcVbDsVSMDczvfnA3uBMQXbfJKO/zMamPXfrT/6UmTbP6JjHrrGgmUJeH/Wf49y96YHvarZc6aE82YF8N0uy2ruvAG+BPymyLp6/54p2psi29fNd82helPP3zUlnDf18l3zt8CvD7I+gOeBzxUsGwHsBD7c+f7Uzt7MKtjm3cA+YHy5/i4OLeidG4B/Tynd02X5TDr+S+SN5SmlJ4DngNbORa3AoymlzQWfuwsYDpzebxWXR7G+dGcE0J5S6nq14IaI2BoRSyPi4xG/f7BzlTtUb/648++9OiL+JiKGFKyr5XMGenjeRMRMoBn4bnf7qMHz5qSI2BgR6zp/ZXdc5/J6/56B4r3pTr191xyqN/X8XdOj86bOvmsuBB6OiP/TOZRkRUR8omD9ZGAs+3/fvAosYf/vm1dSSg8XfO4eOoLsnH6tvoBDC3qoczzMDGB2N6vHArtTSl1/1bC5c11+m83drKdgm6pziL503XYU8Fd0/Nqh0BeBe+n4Vde7gBvpuFp3XZ8WW2Y96M0C4FlgIzAd+CpwCvCHnetr8pyB3p03wKXA4ymlh7osr8XzZgnwMeBJOn5ddzXw64iYRh1/z3Qq2puU0rbCDevtu4ZD96Zuv2voxXlDfX3XTAE+BXwD+J90fBdfFxG7U0q38Pt/9+7Oi8LvmxcKV6aU9kTES5TxvDHI9kBETAS+BcxLvx8XUvd605eIGE7HGKzH6PhVzxtSSl8peLsiIobSMUapar8ketKblFLh/8k+GhHPA7+IiBNSSmvLUWcWenneDKZjrNVXuq6rxfMmpVQ4Lm9VRCyhI4B8CHg9m6oqwyF688YVtHr7roFD96Zev2ugV+dNXX3X0HGz/8MppfwY6BWd/8H8SeCW7MrqPYcW9MxMYDTwSETsiYg9wDnApzv/vBkYGBEju3xuDB2D5+n8Oaab9RRsU20O2pfOGwiIiGF0DJLfBnwgpZQ7xH6XABMiYlA/1t7fetSbLpZ0/jyx82ctnjPQu95cBAyh48aTQ6mF82Y/nVdfn6LjnNhEfX7PdKtLb4C6/a45QHe96aJevmsOcJDe1Nt3zfN0/MdeoceB/LCL/L97d+dF4ffN6MKV0THTxdGU8bwxyPbML4A30zF2Jv96mI679fJ/zgHn5j8QEafQcUK0dS5qA94cEYX/6POAdg48marFQfuSUtrbeXXkbjpuUrmwh1e0m4GXU0q7+qfssjhkb7r5THPnz+c7f9biOQO9682lwJ0ppS092G8tnDf76ZzG5gQ6zonl1Of3TLe69IY6/q45QNfedKNevmsOcJDe1Nt3zYN0DC8pdDIdV6uhY5aCTez/fTOcjrGvhd83IzvHFue9k45suYRyyfrOuWp9ceAd6P+3vfuLkass4zj+/dkGq9l4QYJgVKwpsdGA1ZjqBTGxgloVqRL1Qm7UoMYbE8GooATBpFFCYkwI3JHqhYghgGlTizWSJlpJShaBGxGsW/zTKrEQS6W1oY8X79lwGCa7bOzscjrfTzLZnfO+c+acN2fOPvPkfZ+9lXYBbKJlnPYCe3vtq4BHaBPoNwAfos0t2brS5zKpcaEtFLifVlppHW3OzPxjVdfnY8AVwPm0b8hfBo4C16/0uUx4bNbR5vC9C1hLm3j/J2DPtF0zo2PT23YebdHA5jH9T8vrBriJlp1eSyuDtJtWFuesrn1q7zMLjc2032sWGZupvtcs9pnq+kzjvWYjz5dXO482reIocHmvzzdo5bgupSUf7gH2A2t6fX4BzALvppUB/CPwk2U9l5UezKE+eHEgu4a2CvtwdzHcBZwz8po3ATtpE8af7D5gq5fzuJdzXID30UpzjHus7fpsppU7OQI8A/yeVlf0FSt9LhMemzcCe4B/0cqZPAbcCLxm2q6Z0bHpbdtKW5H/omvhdL1ugJ/SFuQcB/7aPV/Xa5/a+8xCYzPt95pFxmaq7zWLfaa6PlN3r+nO7RLaF5hjtGkFXxhpD3ADLTN7jFaR4C0jfc6kLSY8QivXdhsws5znke5AJEmSpEFxjqwkSZIGyUBWkiRJg2QgK0mSpEEykJUkSdIgGchKkpZwDNwAAAOaSURBVCRpkAxkJUmSNEgGspIkSRokA1lJkiQNkoGsJC2TJJXk4yt9HJJ0ujCQlaT/U5JtXZBaSU4k+UeS3Uk+n6R/n30d7X+Tv5R9GvRK0iIMZCXp1NhFC1TXAh8G7gN+COxIshqgqg5V1fEVO0JJOs0YyErSqXG8C1T/VlWzVbUV2EILaj8LL8yyJjkjyc1JDiY5luRAkqu7trlun3d3r5nrtq9L8vMu4/tMkn1JLu4fRJK5JNckuS3JkSRPJPniSJ83JLk9yeEkR5M8kOQ9vfYtSWa749qf5Lr5YFySXk4MZCVpQqrq18BDwGVjmr8CXAp8GlgPXA7MdW0bu5+fo2V555/PADuBi4B30rLA25OcO7Lvq4AHuj63ALcmWQ+QZAbYA7y+e/8NwI10fw+SvBf4MS2b/DbgS7RA/FtLHgBJmjC/YUvSZP0BePuY7ecCjwG/qaoCDsw3VNWTSQCerqpDve0P0QLjedcm+QQtIL25t31nVd0CkOT7wFeBTcCjwGeAs4CNVXW46/9477XXAd+rqh91z/cnuZYW7F6/lBOXpEkzkJWkyQpQY7ZvA3YDjybZBeyoql8uuKOWTf0O8FFapnY18CpaUNz38PwvVVVJDgGv7Ta9A3iwF8SO2gBcmKSfgV0FrEny6qr6z0LHKEnLyUBWkibrrcCfRzdW1WySN9Pm0F4M/CzJr6rqkwvs6ybgA8DXaFnUZ4E7gTNG+p0YfTuen0r27CLHO0PLyt41pu3YIq+VpGVlICtJE5Lk/cAFwA/GtVfVv4E7gDuS3AnsSnJmly09QcuE9l0IbKuqu7v9z9CqJCzFw8AVvfcZNQusr6rHx7RJ0suKgawknRqvTHIOLfg8G9gMXA3soC2eeoEkVwIHgQeBk8CngEPA012XOeCiJL+lVUR4ijan9rIk22lZ1u+y9EW7twPXAPd0VRIO0haF/b2qfgfcQCsZ9gQt23uSNt3g/Kr69hLfS5ImyqoFknRqbKYFhXO0agKbaJUJtlTVc2P6HwG+TqsusI+WWf1IVZ3s2q+iTSP4Cy3YBbgSeArYC2wH7qVlUF+yqvov8EHgn7QKCI8A3wSe69rvBS7p+uwD7qctFjswbn+StJLSFstKkiRJw2JGVpIkSYNkICtJkqRBMpCVJEnSIBnISpIkaZAMZCVJkjRIBrKSJEkaJANZSZIkDZKBrCRJkgbJQFaSJEmDZCArSZKkQTKQlSRJ0iD9DzJnb5sgT7j3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ce6fe10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6), dpi=100)\n",
    "d_max = 451\n",
    "#plt.plot(d[425:d_max+1], [int(x) for x in intI][425:d_max+1], 'k')\n",
    "plt.plot(d[400:600], [int(x) for x in intI][400:600], 'k')\n",
    "plt.grid()\n",
    "plt.xlabel('Distance')\n",
    "plt.ylabel('Information');\n",
    "#plt.axis([0, 1000, 0, 1000]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
